{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Processes the Functional Way\n",
    "Courtesy David Rosen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These next few functions provide the basic functionality we'll need to work with GPs:  computing the parameters of a joint finite-dimensional distribution, sampling from a multivariate Gaussian, and computing the posterior mean and covariance functions after observing some data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Given mean and covariance *functions* m(*) and k(*,*) for a Gaussian process on a space S, and a vector of points X in S,\n",
    "# this function computes and returns the pair (M_X, K_XX) containing the mean *vector* M_X and covariance *matrix* K_XX for \n",
    "# the joint *finite-dimensional* Gaussian distribution of function values F_X over those points\n",
    "\n",
    "# Q: computes the value of functions m.k in points X? From functions to vectors\n",
    "def compute_finite_dimensional_joint_distribution(m, k, X):\n",
    "    # Construct the mean vector M_X, in which M_X[i] = mu(x_i)\n",
    "    M_X = np.array([m(xi) for xi in X])\n",
    "    \n",
    "    # Construct the covariance matrix K_XX, in which K_XX[i,j] = k(xi, xj)\n",
    "    K_XX = np.zeros( (len(X), len(X)))\n",
    "    for i, xi in enumerate(X):\n",
    "        for j, xj in enumerate(X):\n",
    "            K_XX[i,j] = k(xi, xj)\n",
    "    \n",
    "    return (M_X, K_XX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Draw a sample from the Gaussian process GP(m, k) over the points in the vector X\n",
    "def sample_Gaussian_process(m, k, X):\n",
    "    \n",
    "    # Get the parameters for the finite-dimensional distribution over the points X\n",
    "    FD_params = compute_finite_dimensional_joint_distribution(m, k, X)\n",
    "    \n",
    "    # Draw a sample from this finite-dimensional distribution\n",
    "    #Q: FD_params[0] - finite-dimensional mean\n",
    "    #Q: FD_params[1] - finite-dimensional covariance\n",
    "    return np.random.multivariate_normal(FD_params[0], FD_params[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given the mean and covariance functions mu and k for a (prior) Gaussian process, and vectors of observed inputs and outputs X and F,\n",
    "# this function computes and returns the mean and covariance functions for the posterior GP conditioned on the data X and F\n",
    "def compute_posterior_GP(m, k, X, F):\n",
    "    \n",
    "    # Construct parameters (M_X, K_XX) for the *finite-dimensional* distribution of function values F_X over the data points X under the prior GP\n",
    "    prior_FD_params = compute_finite_dimensional_joint_distribution(m, k, X)\n",
    "    M_X = prior_FD_params[0]\n",
    "    K_XX = prior_FD_params[1]\n",
    "    \n",
    "    # Compute coefficient vector alpha = K_XX^-1 * (F - M )\n",
    "    alpha = np.linalg.solve(K_XX, F - M_X)\n",
    "    \n",
    "    # Construct helper function k_X(x) (returns the N x 1 vector of kernel products [k(x_i, x)]).  \n",
    "    # Note that we include a second (dummy) variable a with default value X to get Python to capture the value of X\n",
    "    k_X = lambda x : np.array([k(xi, x) for xi in X])\n",
    "    \n",
    "    # Construct posterior mean function\n",
    "    mbar = lambda x: m(x) + alpha.dot(k_X(x))\n",
    "    \n",
    "    # Construct posterior covariance function\n",
    "    kbar = lambda x,y: k(x,y) - k_X(x).dot(np.linalg.solve(K_XX, k_X(y)))\n",
    "    \n",
    "    return (mbar, kbar)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up data for GP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = .2\n",
    "s = .5\n",
    "\n",
    "# GP prior mean function: geneally increasing up and to the right, with a periodic component\n",
    "mu = lambda x : .5 * x + np.sin(2 * math.pi * x)\n",
    "\n",
    "# GP prior covariance function: we take the usual squared exponential kernel\n",
    "#k = lambda x,y : s * np.exp(- (x-y) ** 2 / (2*l**2))\n",
    "\n",
    "# GP prior covariance function: we take the usual squared exponential kernel\n",
    "k = lambda x,y : s*(1 + (np.sqrt(3)*(np.abs(x-y))) / l) *np.exp(- (np.sqrt(3)*(np.abs(x-y))) / l)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample a few realizations of a GP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102972d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sample a few realizations of a GP\n",
    "X = np.linspace(0, 3, 500)\n",
    "\n",
    "\n",
    "F1 = sample_Gaussian_process(mu, k, X)\n",
    "F2 = sample_Gaussian_process(mu, k, X)\n",
    "F3 = sample_Gaussian_process(mu, k, X)\n",
    "\n",
    "plt.plot(X, F1, X, F2, X, F3)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe some values and compute the posterior GP mean and covariance functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xtrain = [1, 1.5, 2.5]\n",
    "Ytrain = [2, 3, 4]\n",
    "\n",
    "posterior_GP_params = compute_posterior_GP(mu, k, Xtrain, Ytrain)\n",
    "\n",
    "mbar = posterior_GP_params[0]\n",
    "kbar = posterior_GP_params[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a few samples from the posterior GP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x100c038d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F4 = sample_Gaussian_process(mbar, kbar, X)\n",
    "F5 = sample_Gaussian_process(mbar, kbar, X)\n",
    "F6 = sample_Gaussian_process(mbar, kbar, X)\n",
    "\n",
    "plt.plot(X, F4, X, F5, X, F6)\n",
    "plt.plot(Xtrain, Ytrain, 'r*')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Processes with two-dimensional input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 1.0\n",
    "s = 0.1\n",
    "\n",
    "# GP prior mean function: geneally increasing up and to the right, with a periodic component\n",
    "mu = lambda x : 0\n",
    "\n",
    "# GP prior covariance function: we take the usual squared exponential kernel\n",
    "#k = lambda x,y : s * np.exp(- np.dot((x-y).transpose(),(x-y)) / (2*l**2))\n",
    "k = lambda x,y : s * np.exp(- np.dot((x-y).transpose(),(x-y)) / (2*l**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xtrain = np.array([[1.,1.], [1.5, 2], [1.2, 1.3]])\n",
    "Ytrain = [2, 3, -1.0]\n",
    "\n",
    "posterior_GP_params = compute_posterior_GP(mu, k, Xtrain, Ytrain)\n",
    "\n",
    "mbar = posterior_GP_params[0]\n",
    "kbar = posterior_GP_params[1]\n",
    "\n",
    "nx  = 10\n",
    "ny = 10\n",
    "x = np.linspace(0, 2, nx)\n",
    "y = np.linspace(0, 3, ny)\n",
    "xx, yy = np.meshgrid(x, y)\n",
    "N = nx * ny\n",
    "xv = np.reshape(xx, (N,1))\n",
    "yv = np.reshape(yy, (N,1))\n",
    "Xtest = np.hstack((xv,yv))\n",
    "\n",
    "F7 = sample_Gaussian_process(mbar, kbar, Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2)\n"
     ]
    }
   ],
   "source": [
    "print Xtest.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1027b2c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "#%matplotlib notebook\n",
    "\n",
    "fig = plt.figure(figsize=(10,4))\n",
    "ax = plt.subplot(111, projection='3d')\n",
    "ax = plt.subplot(121, projection='3d')\n",
    "\n",
    "ax.scatter(Xtrain[:,0], Xtrain[:,1], Ytrain, s=20, c='r')\n",
    "ax.scatter(Xtest[:,0], Xtest[:,1], F7, s = 10, c=F7)\n",
    "\n",
    "ax2 = plt.subplot(122, projection = '3d')\n",
    "\n",
    "zz = np.reshape(F7, (nx,ny))\n",
    "ax2.plot_surface(xx, yy, zz, rstride=1, cstride=1, cmap='viridis',linewidth=0, antialiased=False)\n",
    "ax2.scatter(Xtrain[:,0], Xtrain[:,1], Ytrain, s=20, c='r')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multi-dimensional input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5, 1)\n",
      "Prediction 0.04899137253165379\n"
     ]
    }
   ],
   "source": [
    "Xtrain = np.array([\n",
    "    [0,0,2,0,0.04], #0\n",
    "    [1,0,2,0,0.04], #1\n",
    "    [1,1,2,0,0.04], #2\n",
    "    [1,0,1,0,0.04], #3\n",
    "    [0,0,1,0,0.04], #4\n",
    "    [0,0,3,0,0.04]  #5\n",
    "])\n",
    "Ytrain = np.array([0.357,0.362,0.373,0.346,0.346,0.340])\n",
    "\n",
    "posterior_GP_params = compute_posterior_GP(mu, k, Xtrain, Ytrain)\n",
    "mbar = posterior_GP_params[0]\n",
    "kbar = posterior_GP_params[1]\n",
    "\n",
    "#Xtest = np.array([[1,0,2,2,0.04], [1,0,2,0,0.04]])\n",
    "Xtest = np.array([[1,0,2,2,0.04]]) #6\n",
    "print (Xtest.transpose()).shape\n",
    "#Ytest = sample_Gaussian_process(mbar, kbar, Xtest)\n",
    "Ytest = mbar(Xtest[0,:])\n",
    "print \"Prediction\", Ytest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5]\n",
      "[0.357 0.362 0.373 0.346 0.346 0.34 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10284c690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "re_x = np.arange(0,len(Ytrain))\n",
    "print re_x\n",
    "print Ytrain\n",
    "\n",
    "fig = plt.figure(1)\n",
    "\n",
    "plt.plot(re_x, Ytrain)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
